/**
 * Exact bounding box calculation for paths with bezier curves
 *
 * Bezier curves can extend beyond their control points, so we need to find
 * the actual extrema by solving for where the derivative equals zero.
 */
import type { GlyphPath } from "../render/path.ts";
/**
 * Bounding box in 2D space
 */
export interface BBox {
    xMin: number;
    yMin: number;
    xMax: number;
    yMax: number;
}
/**
 * Calculate exact bounding box for a path
 *
 * For line segments: min/max of endpoints
 * For quadratic bezier: find t where derivative = 0, evaluate curve at those t values
 * For cubic bezier: solve quadratic for extrema, evaluate curve at those t values
 *
 * @param path - Path to calculate bounds for
 * @returns Bounding box or null for empty path
 */
export declare function getExactBounds(path: GlyphPath): BBox | null;
/**
 * Find t values where a quadratic bezier has extrema
 *
 * For quadratic bezier B(t) = (1-t)²p0 + 2(1-t)t*p1 + t²p2
 * Derivative: B'(t) = 2(1-t)(p1-p0) + 2t(p2-p1)
 *                   = 2(p1-p0) + 2t(p0-2p1+p2)
 *                   = 2[(p1-p0) + t(p0-2p1+p2)]
 *
 * Set B'(t) = 0:
 * (p1-p0) + t(p0-2p1+p2) = 0
 * t = -(p1-p0)/(p0-2p1+p2)
 *   = (p0-p1)/(p0-2p1+p2)
 *
 * @param p0 - Start point
 * @param p1 - Control point
 * @param p2 - End point
 * @returns Array of t values in [0,1] where extrema occur
 */
export declare function getQuadraticExtrema(p0: number, p1: number, p2: number): number[];
/**
 * Find t values where a cubic bezier has extrema
 *
 * For cubic bezier B(t) = (1-t)³p0 + 3(1-t)²t*p1 + 3(1-t)t²p2 + t³p3
 * Derivative: B'(t) = 3(1-t)²(p1-p0) + 6(1-t)t(p2-p1) + 3t²(p3-p2)
 *
 * Simplified: B'(t) = at² + bt + c where:
 * a = 3(p3 - 3p2 + 3p1 - p0)
 * b = 6(p2 - 2p1 + p0)
 * c = 3(p1 - p0)
 *
 * Solve using quadratic formula: t = (-b ± √(b²-4ac)) / 2a
 *
 * @param p0 - Start point
 * @param p1 - First control point
 * @param p2 - Second control point
 * @param p3 - End point
 * @returns Array of t values in [0,1] where extrema occur
 */
export declare function getCubicExtrema(p0: number, p1: number, p2: number, p3: number): number[];
/**
 * Evaluate quadratic bezier at parameter t
 *
 * B(t) = (1-t)²p0 + 2(1-t)t*p1 + t²p2
 *
 * @param p0 - Start point
 * @param p1 - Control point
 * @param p2 - End point
 * @param t - Parameter in [0,1]
 * @returns Value at t
 */
export declare function evaluateQuadratic(p0: number, p1: number, p2: number, t: number): number;
/**
 * Evaluate cubic bezier at parameter t
 *
 * B(t) = (1-t)³p0 + 3(1-t)²t*p1 + 3(1-t)t²p2 + t³p3
 *
 * @param p0 - Start point
 * @param p1 - First control point
 * @param p2 - Second control point
 * @param p3 - End point
 * @param t - Parameter in [0,1]
 * @returns Value at t
 */
export declare function evaluateCubic(p0: number, p1: number, p2: number, p3: number, t: number): number;